T1 Project 3: Fill & Download for Free

**** Irritate each other if there are 2 inside 😂😝🥰😍 ****I can never forget that day, anomaly scan during my wife’s pregnancy. We reached our Foetal Medicine specialist at around 11 am to start with the procedure. The doc had named our then fetuses' T1 and T2 i.e. short for Twin 1 and Twin 2 for ease of discussion.T2 turned out to be an obedient foetus and the doc identified all crucial anatomical stuff such as lips, nose, eyes, ears, digits and so on. Now was T1’s turn. But..But..But..T1 was hiding her face(her coz we know the gender now😂😂) and repeated nudges by the doc through the handheld probe failed to wake her up. The doc asked my wife to come back after a stroll but even this failed as T1 wouldn’t show her face even now. She now asked my wife to intake some calories in form of chocolate shake etc. but guess what… T1 was still sleeping !!!!!Now T2 comes into action and it was so cute to witness this live👶💪😍T2 kicked T1 through her Amniotic sac. T1 kept sleeping. T2 then placed her hand on T1’s head. T1 gently removed T2’s hand from her head and kept sleeping!!!It was 3 pm by now and for the first time in my life I could see a Doc getting impatient. Ultimately she managed a way to identify T1’s facial organs through some projections etc. and we just prayed to the almighty that all turns out well.STAY BLESSED ALL OF YOU ALWAYS AND ALWAYS🥰🥰🥰 !!!!!

Recall that Ranges are same for ϴ and 90- ϴ[math]T1=(2uSin(ϴ)/g) ----eq(1)[/math][math]T2=(2uSin(90-ϴ)/g)----eq(2)[/math]Since[math] Sin(90-ϴ)=Cos(ϴ)[/math]so we can write eq(2) as[math]T2=(2uCos(ϴ)/g)----eq(3)[/math]Now multiplying eq(1) & eq(3)we get[math]T1*T2=(4u^2Cos(ϴ)Sin(ϴ)/g^2) ----eq(4)[/math]Using the identity[math]Sin(2ϴ)=2Sin(ϴ)Cos(ϴ)[/math]Now eq(4) becomes[math]T1*T2=(2u^2Sin(2ϴ)/g^2)[/math]Since Range=[math] (u^2Sin(2ϴ)/g)[/math][math]T1*T2=2R/g[/math][math]R=T1*T2*g/2[/math]

I’m going to read “genius” as “hardest, most fiddly, confusing thing I ever did”Long story short: It’s a GLSL shader used by a three.js webapp. You can see the code here. The rendered output looks like this:GIFs don’t work well on Quora, but you can see the rendered app here (Fair warning, it’s total garbage on mobile devices. Personal project from 3 year ago. Not my fault, they hadn’t invented cell phones in 2017).Longer story:I wanted to render Earth’s near solar neighborhood; a 3D, accurate map of all stars within 50 lightyears of earth. Something like this:Except a version rendered in a browser, explorable, and which didn’t look like a cut-scene from NetHack.I actually did manage to do this. In the process, I used placeholder graphics for the stars themselves,Because I had accidentally actually finished a personal project, I had the brilliant idea, to make sure the project was never quite done, to “make stars look more real.” Basically, I wanted toUse the star’s temperature (stars range from 2500 Kelvin up to about 50,000 Kelvin) to accurately render color.Display other gradients, noise functions, and other Weird Stuff so the star looks more like a stellar bag of exploding hydrogen and less like a spherical cow.You don’t stare at the sun very often. For good reason — your eyeballs will be seared out of your skull and you’ll melt into toxic goo like the Nazis in Raiders of the Lost Arc. But if you did — very carefully — study the sun, it would look like this:There’s a lot going on there. There are hot spots. Cold spots. Swirly bits. Flamey bits (you can tell I’m a scientist).I wanted to render it all, or at least a plausible version of it.Most three.js code works like normal, Turing-complete, functional, looping code, like good honest JavaScript: var geometry = new THREE.Geometry();  geometry.vertices.push(new THREE.Vector3(0, 0, 0));  geometry.vertices.push(new THREE.Vector3(.05, 0, .01));  var labelLine = new THREE.Line(geometry, lineMaterial); Look at that. Objects. Numbers. Variables. Just like god intended.Unfortunately, three.js JavaScript geometries can only get you so far. What they cannot draw are textures. Three.js without textures can draw sophisticated, accurate, efficiently rendered…. spheres:(please, hold your applause until the end)To render textures in three.js by implementing pixel and fragment shaders, you have to whisper sweet nothings at the GPU in a very special language: GLSL.Unless you’ve been living in a cave on the far side of the moon, you know that GPUs have eaten the world. (web-dev, 2019 — “if you aren’t using a GPU, are you even trying?”)GPUs are kind of dumb. You can’t just tell them to run code. You have to speak in very simple sentences and cut their data into tiny little bits so they don’t choke on a variable and die. But if you do it right… they can render images orders of magnitude faster than a CPU.Unlike JavaScript, GLSL code runs directly on the GPU. GLSL is not normal. It is not fun. It doesn’t (really) have concepts we take for granted in CS 101, like…. loops, recursion, or libraries. You’re just writing large blobs of strongly-typed math.To color a pixel — the fundamental goal of a shader — you write a fragment shader that looks like this:varying vec3 vTexCoord3D; uniform float time;  void main( void ) {  ???  gl_FragColor = vec4(vec3(r g, b), a); } You get a few variables in and write a 4vector, with a specific color, out. I wanted to render all the features I saw in IRL solar photoimagery — granules, sunspots, hot areas, cold areas, coronas, etc.I’m struggling here, because I remember so little of how this code works. It’s a mix of static noise functions I found online, decomposed bitmaps translated into C code, and various fiddling to add the sunspots and features I wanted. I’d love to, for example, explain what float frequency = 0.04;  float t1 = snoise(vTexCoord3D * frequency)*2.7 - 1.9;  float brightNoise= snoise(vTexCoord3D * .02)*1.4- .9;  float ss = max(0.0, t1);  float brightSpot = max(0.0, brightNoise);  float total = noiseBase - ss + brightSpot;  float temp = (highTemp * (total) +(1.0-total) * lowTemp);  float i =(temp - 800.0)*0.035068; means, but I just get a strange hissing in my ears when I look directly at the code. Instead, I’ll just point to a summary I wrote shortly after writing the code — you can find it here.Either way, it works, and I was pretty thrilled with the result. I’m not an astronomer, so I’m not going to claim the rendered images are accurate, but they are at least… cool:GLSL is probably not something I’ll ever need to write again. But it was fun learning a bit about GPU processing, and I got to write some of the weirdest, densest, math-iest code I’ll (luckily) ever touch.